Gamma-convergence of fractional Gaussian perimeter

created by carbotti on 30 Mar 2021
modified on 20 Sep 2021

[BibTeX]

Accepted Paper

Inserted: 30 mar 2021
Last Updated: 20 sep 2021

Journal: Advances in Calculus of Variations
Pages: 30
Year: 2021

ArXiv: 2103.16598 PDF
Notes:

30 pages, 3 figures

Abstract:

We prove the $\Gamma$-convergence of the renormalised fractional Gaussian $s$-perimeter to the Gaussian perimeter as $s\to 1^-$. Our definition of fractional perimeter comes from that of the fractional powers of Ornstein-Uhlenbeck operator given via Bochner subordination formula. As a typical feature of the Gaussian setting, the constant appearing in front of the $\Gamma$-limit does not depend on the dimension.